1. Field of the Invention
The present invention relates to a developing method for developing an electrostatic latent image on an image support into a visible image, in an image-formation apparatus of an electronic photographing system.
2. Description of the Prior Art
(Prior Art 1)
A photosensitive unit as an image support on which an electrostatic latent image is formed can be expressed by a model consisting of a resistance component xcex94Rv and a capacity component xcex94Cp in a thickness direction respectively and a resistance component xcex94Rs in a surface direction as shown by an equivalent circuit in FIG. 2. Therefore, if the resistance component xcex94Rs is sufficiently high, an electric charge accumulated in the capacity component xcex94Cp, that is, an electrostatic latent image, can be held during a period between finish of an exposure and finish of a development. However, when the resistance component xcex94Rs has become lower due to an adhesion of a stain or the like, the electric charge accumulated in the capacity component xcex94Cp is lost. As a result, it becomes impossible to obtain a desired resolution.
This state is shown in FIG. 3. FIG. 3 shows one example of a diffusion along a lapse of time of an electrostatic latent image that has been formed with an edge located at a position of x=0. It can be understood from FIG. 3 that there occurs a leakage of an electric charge in the surface direction and the electrostatic latent image changes along with a lapse of time.
As a publication that introduces a prior art of investigation carried out into the resolution of a photosensitive unit from the viewpoint of a change in the electrostatic latent image due to a diffusion of an electric charge along with the lapse of time, there is xe2x80x9cA study in the resolution characteristics of a photosensitive unit based on analysis of an electrostatic latent imagexe2x80x9d, Electronic Photograph Academy Magazine, Volume 30, No. 4, 1991, pp. 432-438. This publication reports on a result of a simulation carried out for the deterioration in the resolution of an electrostatic latent image along with a lapse of time based on an electrostatic capacity of a photosensitive unit and a resistance of a charged member. A potential change on a photosensitive unit is expressed by the following.
(xcex4V/xcex4t)=(1/(Rsxc2x7Cp))xc2x7(xcex4V2/xcex4x2)xe2x88x92V/(Rvxc2x7dxc2x7Cp)xe2x80x83xe2x80x83(1)
A general solution of this expression is given as follows.
V=Vs(x, t)xc2x7exp(xe2x88x92t/(Rvxc2x7dxc2x7Cp))xe2x80x83xe2x80x83(2)
Further, an edge width W of a one-dimensional electrostatic latent image is given as follows.
W=3.55(t/(Cpxc2x7Rs))xc2xdxe2x80x83xe2x80x83(3)
(Prior Art 2)
Various results of investigations have been announced that model a development area and express development characteristics by a numerical equation in an attempt to optimize the development characteristics that are determined based on a combination of a potential of a photosensitive unit, a thickness of a toner layer, a toner charge volume, a resistance of a developing roller, a development bias, etc. As a representative prior art of this trial, there is xe2x80x9cA contact type component nonmagnetic development system (1)xe2x80x9d, Electronic Photograph Academy Magazine, Volume 31, No. 4, 1992, pp. 531-541. According to this method, the electric field of the development area is obtained from a Poisson equation, and a development equation and a simulation result are reported. As a development equation in the case of using a semiconductive developing roller, the following expression is shown.
msi=(1/A)xc2x7(mc+kxc2x7mo/A)xc2x7(qp/q)xc2x7R1)/(1+(1/(Axc2x7k)xc2x7R1))xe2x80x83xe2x80x83(4)
where
A=dp/∈p+dt/∈txe2x80x83xe2x80x83(5)
mc=(1/A)xc2x7(xe2x88x92(Voxe2x88x92Vb)/q+(kxc2x7mo/2)xc2x7(dt/∈t))xe2x80x83xe2x80x83(6)
The prior art 1 is based on a simulation that assumes that the development potential is at an intermediate point between the potential of an unexposed portion (VH in the case of an inversion development) and the potential of an exposed portion (VL in the case of an inversion development). The prior art 1 has no disclosure about a correlation with an optional latent image potential. Therefore, there is a problem in that it is not possible to understand a resolution at an optional latent image potential based on an actual using state, such as a development potential at which a highest resolution can be obtained leaving the characteristics of a photosensitive unit as it is, or a development potential that can guarantee the initial performance despite adhesion of stain.
According to the prior art 2, a development current that flows based on the charge qp generated by a frictional charging of a development nip portion is treated with too much emphasis. Further, there is a problem in that no consideration has been taken into the resistance at the photosensitive unit side.
In the light of the above problems, it is, therefore, an object of the present invention to provide a developing method capable of realizing a satisfactory image quality in high resolution, based on a setting of a development condition that takes into account the charge diffusion of a latent image due to a surface resistance of an image support.
In order to achieve the above object, the present invention is configured as follows:
In accordance with the first aspect of the present invention, a developing method for developing an electrostatic latent image formed on an image support, by an inversion development is characterized in setting the following relationship:
abs(V1) less than abs(Vth)
where abs (X) represents an absolute value of X,
when
V1=(0.348 Wr2xe2x88x921.161 Wr+1.0163) Vo,
and
Wr=(1/3.63)xc2x7(Rsxc2x7Cp/t)xc2xdxc2x7W,
where
Cp (F/m2) represents an electrostatic capacity of an image support, Rs (xcexa9) represents a surface resistance, t (sec) represents a moving time from an electrostatic latent image formation area to a development completion area, Vo (V) represents a potential of a non-image portion of an electrostatic latent image in an image area at the time of forming the electrostatic latent image, Vth (V) represents a surface voltage of the image support when a developing member starts a development at a saturated latent image potential in a solid image, W (m) represents a desired minimum image width, and V1 (V) represents a marginal latent image potential in the minimum image width.
In accordance with the second aspect of the present invention, the developing method having the above first aspect is further characterized in setting the following relationship:
abs(V1xe2x80x2) less than abs(Vth)
when
V1xe2x80x2=V1xc2x7exp(xe2x88x92t/(Rvxc2x7Cp))
where
Rv (xcexa9xc2x7m2) represents a resistance of the image support in a thickness direction.
In accordance with the third aspect of the present invention, the developing method having the above first aspect is further characterized in that, when a toner layer is formed on the surface of the developing member that is applied with a bias voltage Vb (V), and when this developing member is brought into a sliding contact with the image support by a development nip of a predetermined width, values of the following parameters are adjusted to satisfy the following relationship:
(xe2x88x92V1+nxc2x7Vt+Vb)/xcfx81d greater than 0
where
xcfx81d represents a charge density of the toner layer immediately after the image support passes through the development nip, Vt (V) represents a potential of the toner layer on the developing member, Rr (xcexa9xc2x7m2) represents a resistance of the developing member, and n represents a ratio (vb/vp) of a rotational speed vb (m/sec) of the developing member to a rotational speed vp (m/sec) of the image support.
In accordance with the fourth aspect of the present invention, the developing method having the above third aspect is further characterized in that values of the following parameters are adjusted to satisfy the following relationship:
(xe2x88x92(V1+dV)+nxc2x7Vt+Vb)/xcfx81d greater than 0
where
dV (V) represents a variation in the surface potential of the image support due to a friction with the toner when the surface of the image support passes through the development nip.
In accordance with the fifth aspect of the present invention, the developing method having the above second aspect is further characterized that, when a toner layer is formed on the surface of the developing member that is applied with a bias voltage Vb (V), and when this developing member is brought into a sliding contact with the image support by a development nip of a predetermined width, values of the following parameters are adjusted to satisfy the following relationship:
xe2x80x83(xe2x88x92V1xe2x80x2+nxc2x7Vt+Vb)/xcfx81d greater than 0
where
xcfx81d represents a charge density of the toner layer immediately after the image support passes through the development nip, Vt (V) represents a potential of the toner layer on the developing member, Rr (xcexa9xc2x7m2) represents a resistance of the developing member, and n represents a ratio (vb/vp) of a rotational speed vb (m/sec) of the developing member to a rotational speed vp (m/sec) of the image support.
In accordance with the sixth aspect of the present invention, the developing method having the above fifth aspect is further characterized in that values of the following parameters are adjusted to satisfy the following relationship:
(xe2x88x92(V1xe2x80x2+dV)+nxc2x7Vt+Vb)/xcfx81d greater than 0
where
dV (V) represents a variation in the surface potential of the image support due to a friction with the toner when the surface of the image support passes through the development nip.
In accordance with the seventh aspect of the present invention, a developing method for developing an electrostatic latent image formed on an image support by a positive development is characterized in setting the following relationship:
abs(V2) less than abs(Vth)
where abs (X) represents an absolute value of X,
when
V2=(xe2x88x920.348 Wr2+1.161 Wrxe2x80x940.0163))Vo,
and
Wr=(1/3.63)xc2x7(Rsxc2x7Cp/t)xc2xdxc2x7W,
where
Cp (F/m2) represents an electrostatic capacity of an image support, Rs (xcexa9) represents a surface resistance, t (sec) represents a moving time from an electrostatic latent image formation area to a development completion area, Vo (V) represents a potential of a non-image portion of an electrostatic latent image in an image area at the time of forming the electrostatic latent image, Vth (V) represents a surface voltage of the image support when a developing member starts a development at a saturated latent image potential in a solid image, W (m) represents a desired minimum image width, and V2 (V) represents a marginal latent image potential in the minimum image width.
In accordance with the an eighth aspect of the present invention, the developing method having the above seventh aspect is further characterized in setting the following relationship:
abs(V2xe2x80x2) less than abs(Vth)
when
V2xe2x80x2=V2xc2x7exp(xe2x88x92t/(Rvxc2x7Cp))
where
Rv (xcexa9xc2x7m2) represents a resistance of the image support in a thickness direction.
In accordance with the a ninth aspect of the present invention, the developing method having the above seventh aspect is further characterized in that, when a toner layer is formed on the surface of the developing member that is applied with a bias voltage Vb (V), and when this developing member is brought into a sliding contact with the image support by a development nip of a predetermined width, values of the following parameters are adjusted to satisfy the following relationship:
(xe2x88x92V2+nxc2x7Vt+Vb)/xcfx81d greater than 0
where
xcfx81d represents a charge density of the toner layer immediately after the image support passes through the development nip, Vt (V) represents a potential of the toner layer on the developing member, Rr (xcexa9xc2x7m2) represents a resistance of the developing member, and n represents a ratio (vb/vp) of a rotational speed vb (m/sec) of the developing member to a rotational speed vp (m/sec) of the image support.
In accordance with the tenth aspect of the present invention, the developing method having the above ninth aspect is further characterized in that values of the following parameters are adjusted to satisfy the following relationship:
xe2x80x83(xe2x88x92(V2+dV)+nxc2x7Vt +Vb)/xcfx81d greater than 0
where
dV (V) represents a variation in the surface potential of the image support due to a friction with the toner when the surface of the image support passes through the development nip.
In accordance with the eleventh aspect of the present invention, the developing method having the above eighth aspect is further characterized in that when a toner layer is formed on the surface of the developing member that is applied with a bias voltage Vb (V), and when this developing member is brought into a sliding contact with the image support by a development nip of a predetermined width, values of the following parameters are adjusted to satisfy the following relationship:
(xe2x88x92V2xe2x80x2+nxc2x7Vt+Vb)/xcfx81d greater than 0
where
xcfx81d represents a charge density of the toner layer immediately after the image support passes through the development nip, Vt (V) represents a potential of the toner layer on the developing member, Rr (xcexa9xc2x7m2) represents a resistance of the developing member, and n represents a ratio (vb/vp) of a rotational speed vb (m/sec) of the developing member to a rotational speed vp (m/sec) of the image support.
In accordance with the twelfth aspect of the present invention the developing method having the above eleventh aspect is further characterized in that values of the following parameters are adjusted to satisfy the following relationship:
(xe2x88x92(V2xe2x80x2+dV)+nxc2x7Vt+Vb)/xcfx81d greater than 0
where
dV (V) represents a variation in the surface potential of the image support due to a friction with the toner when the surface of the image support passes through the development nip.
In accordance with the thirteenth aspect of the present invention, the developing method having the above first or seventh aspect is further characterized in that values of the following parameters are adjusted to satisfy the following relationship:
Rr/nxe2x89xa6(dt/∈t+dp/∈p)
where
dp (m) represents a thickness of the photosensitive unit layer of the image support, ∈p (F/m) represents a permittivity thereof, dt (m) represents a thickness of the toner layer before the development, ∈t (F/m) represents a permittivity thereof, Rr (xcexa9xc2x7m2) represents a resistance of the developing member, and n represents a ratio (vb/vp) of a rotational speed vb (m/sec) of the developing member to a rotational speed vp (m/sec) of the image support.
In accordance with a fourteenth aspect of the present invention, the developing method having the above thirteenth aspect is further characterized in that, when the image support has a resistance layer of Rp (xcexa9xc2x7m2), values of the following parameters are adjusted to satisfy the following relationship:
Rr/n+Rpxe2x89xa6(dt/∈t+dp/∈p)
In accordance with the fifteenth aspect of the present invention, the developing method having the above first or seventh aspect is characterized in that, when a toner layer is formed on the surface of the developing member that is applied with a bias voltage Vb (V), and when this developing member is brought into a sliding contact with the surface of the image support by a development nip of a predetermined width, values of the following parameters are adjusted to satisfy the following relationship:
xe2x88x92(Vsat+dV)+Vb+nxc2x7Vtxe2x89xa7xcex7xc2x7(nxc2x7dt)xc2x7xcfx81dxc2x7(dt/∈t+dp /∈p+Rr/n+Rp)
where
Vsat (V) represents a saturated value of a potential of an image portion in the image support, dp (m) represents a thickness of the photosensitive unit layer of the image support, ∈p (F/m) represents a permittivity thereof, xcfx81d (C/m) represents a charge density of the toner layer immediately after the surface of the image support passes through the development nip, dt (m) represents a thickness of the toner layer, ∈t (F/m) represents a permittivity thereof, Rr (xcexa9xc2x7m2) represents a resistance of the developing member, dV (V) represents a variation in the surface potential of the image support due to a friction with the toner when the surface of the image support passes through the development nip, n represents a ratio (vb/vp) of a rotational speed vb (m/sec) of the developing member to a rotational speed vp (m/sec) of the image support, and xcex7 represents a permissible value of development efficiency.
In accordance with the sixteenth aspect of the present invention, the developing method having the above fifteenth aspect is further characterized in that Pp or dv is omitted or its value is set to zero (0) when it is possible to disregard a variation in the surface potential of the image support due to a friction with the toner at the time of passing through the development nip, or when the image support does not have a resistance layer or when this can be disregarded.
In accordance with the seventeenth aspect of the present invention, the developing method having the above first or seventh aspect, is further characterized in that, when xcex3=(1/xcex7)xe2x88x921, a resistance Rr of the developing member and a resistance Rp of the resistance layer of the image support are set to satisfy the following relationship:
Rr/n+Rpxe2x89xa6xcex3xc2x7(dt/∈t+dp/∈p).
In accordance with the eighteenth aspect of the present invention, the developing method having the above seventeenth aspect is further characterized in that Pp is omitted or its value is set to zero (0) when the image support does not have a resistance layer or when this can be disregarded.
According to the first aspect, it is possible to set a development starting voltage at which it is possible to draw a marginal value of deterioration in the image quality due to a diffusion of a charge, that is, a marginal value of the resolution. Therefore, by adjusting the development condition based on this development starting voltage, it becomes possible to form an electrostatic latent image according to an original image that is expressed in high resolution. As a result, it becomes possible to realize a satisfactory image quality.
Further, according to the setting of the second aspect, it is possible to obtain a development starting voltage by taking into account a dark attenuation.
Further, when various values are adjusted to satisfy the conditions of the third and fifth aspects, it is possible to obtain a development starting voltage by taking into account a moving rate, a toner layer thickness, etc. When the development starting voltage is set more strictly as explained above, it becomes possible to prevent a reduction in the resolution and to realize a more satisfactory image quality, by reducing the influence of a charge diffusion on the electrostatic latent image of an original image prepared in high resolution.
Further, when various values are adjusted to satisfy the conditions of the fourth and sixth aspects, it is possible to obtain a development starting voltage by taking into account a frictional charging due to a friction between the surface of the image support and the toner in the development nip.
Further, according to the setting of the seventh aspect, it is possible to realize a satisfactory image quality of an original image prepared in high resolution.
Further, according to the development conditions as set in the thirteenth and fourteenth aspects, it is possible to obtain high development efficiency. As a result, it is possible to carry out a stable development.
Further, when various values are adjusted to satisfy the condition of the fifteenth aspect, it is possible to efficiently move the toner that is supplied to the development nip to the image support. Therefore, it becomes possible to guarantee the development efficiency above the expected level. As a result, the toner can be consumed effectively by preventing deterioration of the toner and the adhesion of the toner. This enables to have a long life of the toner and the image support respectively.
Further, according to the setting of the seventeenth aspect, it becomes possible to obtain resistance values to secure high development efficiency. Thus, it is possible to prevent a reduction in the development volume that occurs when each resistance is higher than the set value. As a result, it is possible to increase the development efficiency.